On the Stability of Some Linear Nonautonomous Random Systems

1968 ◽  
Vol 35 (1) ◽  
pp. 7-12 ◽  
Author(s):  
E. F. Infante
Keyword(s):  
Random Systems ◽  
Second Order ◽  
Stability Conditions ◽  
Almost Sure Stability ◽  
Stability Properties ◽  
The Stability ◽  
Second Order Equations

A theorem and two corollaries for the almost sure stability of linear nonautonomous random systems are presented. These results are applied to the study of the stability properties of some often encountered second-order equations and the obtained stability conditions are compared to previously known criteria.

scholarly journals CENTRAL EQUILIBRIA IN MULTILOCUS SYSTEMS. II. BISEXUAL GENERALIZED NONEPISTATIC SELECTION MODELS

Genetics ◽  
1979 ◽  
Vol 91 (4) ◽  
pp. 799-816
Author(s):  
Samuel Karlin ◽  
Uri Liberman
Keyword(s):  
Arithmetic Mean ◽  
Sexual Differences ◽  
Stability Conditions ◽  
Male And Female ◽  
Stability Properties ◽  
Selection Regime ◽  
Existence And Stability ◽  
The Stability ◽  
Linkage Relationships ◽  
Weighted Combination

ABSTRACT This paper is a continuation of the paper "Central Equilibria in Multilocus Systems I," concentrating on existence and stability properties accruing to central H-W type equilibria in multilocus bisexual systems acted on by generalized nonepistatic selection forces coupled to recombination events. The stability conditions are discussed and interpreted in three perspectives, and the influence of sexual differences in linkage relationships together with sex-dependent selection is appraised. In this case we deduce that the stability conditions of the H-W polymorphism in the bisexual model coincide exactly with the conditions for the corresponding monoecious model, provided that the recombination distribution imposed is that of the arithmetic mean of the male and female recombination distributions. A second concern has the same recombination distribution for both sexes, but contrasting selection regimes between sexes. It is then established that, with respect to discerning the relevance of the H-W equilibrium, there is an equivalent monoecious selection regime which is an appropriate "weighted combination" of the male and female selection forms. Finally, in the case where the selection and recombination structures are both sex dependent, a hierarchy of comparisons is elaborated, seeking to unravel the nature of selection-recombination interaction for monoecious versus diocecious systems.

scholarly journals ANALYSIS OF STABILITY OF ONE CLASS OF NUMERICAL METHODS OF SECOND ORDER

2019 ◽  
pp. 92-95
Author(s):  
Vasyl Mykhaylovych Zaiats
Keyword(s):  
Numerical Methods ◽  
Second Order ◽  
Stability Conditions ◽  
Difference Formula ◽  
Conservative Systems ◽  
Trapezoid Method ◽  
The Difference ◽  
Analysis Of Stability ◽  
The Stability ◽  
Combined Numerical Methods

The paper deals with the analysis of the stability of a class of second order combined numerical methods based on the trapezoid method and the difference formula, what obtained by the author. The stability conditions for this class of methods are obtained by the example of conservative systems.

scholarly journals P-Stable Higher Derivative Methods with Minimal Phase-Lag for Solving Second Order Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Fatheah A. Hendi
Keyword(s):  
Oscillatory Behavior ◽  
Multistep Method ◽  
Second Order ◽  
Phase Lag ◽  
Stability Properties ◽  
Higher Derivative ◽  
Orbital Problems ◽  
Algebraic Order ◽  
The Stability ◽  
Physical Phenomena

Some new higher algebraic order symmetric various-step methods are introduced. For these methods a direct formula for the computation of the phase-lag is given. Basing on this formula, calculation of free parameters is performed to minimize the phase-lag. An explicit symmetric multistep method is presented. This method is of higher algebraic order and is fitted both exponentially and trigonometrically. Such methods are needed in various branches of natural science, particularly in physics, since a lot of physical phenomena exhibit a pronounced oscillatory behavior. Many exponentially-fitted symmetric multistepmethods for the second-order differential equation are already developed. The stability properties of several existing methods are analyzed, and a newP-stable method is proposed, to establish the existence of methods to which our definition applies and to demonstrate its relevance to stiff oscillatory problems. The work is mainly concerned with two-stepmethods but extensions tomethods of larger step-number are also considered. To have an idea about its accuracy, we examine their phase properties. The efficiency of the proposed method is demonstrated by its application to well-known periodic orbital problems. The new methods showed better stability properties than the previous ones.

scholarly journals Second Order Equations in Functional Spaces: Qualitative and Discrete Well-Posedness

2015 ◽  
Vol 2015 ◽  
pp. 1-63 ◽  
Author(s):  
A. Ashyralyev ◽  
J. Pastor ◽  
S. Piskarev ◽  
H. A. Yurtsever
Keyword(s):  
Approximate Solution ◽  
Difference Equations ◽  
Second Order ◽  
Difference Schemes ◽  
Well Posedness ◽  
Present Survey ◽  
The Stability ◽  
Well Posed ◽  
Second Order Equations

The present survey contains the recent results on the local and nonlocal well-posed problems for second order differential and difference equations. Results on the stability of differential problems for second order equations and of difference schemes for approximate solution of the second order problems are presented.

REGULARIZED DIFFERENCE SCHEMES FOR EVOLUTIONARY SECOND ORDER EQUATIONS

1992 ◽  
Vol 02 (03) ◽  
pp. 295-315 ◽  
Author(s):  
ALEKSANDR A. SAMARSKII ◽  
PETER N. VABISHCHEVICH
Keyword(s):  
Initial Conditions ◽  
Type Equation ◽  
Second Order ◽  
Difference Schemes ◽  
Inversion Method ◽  
Extension Problem ◽  
Elliptic Type ◽  
The Stability ◽  
Well Posed ◽  
Second Order Equations

The questions of approximate solution of unstable problems for evolutionary second order equations are discussed in this paper. The classical Cauchy problem for elliptic type equation is a significant example of such problem. Incorrectness of this problem (the Hadamard example) is due to instability of the solution towards small perturbations of the initial conditions. The extension problem of the solutions of well-posed elliptic problems beyond the calculation region boundary is also discussed. The stability of corresponding difference schemes is investigated by basing on general theory of ρ-stability. The principle of the regularization of three-layer difference schemes is developed for the unstable problems. It is shown that the regularized difference schemes correspond to some modification of quasi-inversion method.

scholarly journals On the Analysis of Damped Gyroscopic Systems Using Lyapunov Direct Method

2021 ◽  
pp. 63-74
Author(s):  
Ubong D. Akpan
Keyword(s):  
Direct Method ◽  
Stability Conditions ◽  
Lyapunov Direct Method ◽  
Gyroscopic Effect ◽  
Stability Properties ◽  
The Stability ◽  
Gyroscopic Systems

In this work, the stability properties of damped gyroscopic systems have been studied using Lyapunov direct method. These systems are generally stable because of the presence of gyroscopic effect. Conditions for determining the stability of the damped gyroscopic systems have been developed. Solution bounds of amplitude and velocity have been obtained for both homogeneous and inhomogeneous cases. An example is given to show how the stability conditions are applied to systems to determine its stability status.

REPLICATOR DYNAMIC LEARNING IN MUTH'S MODEL OF PRICE MOVEMENTS

2012 ◽  
Vol 18 (3) ◽  
pp. 573-592 ◽  
Author(s):  
Eran A. Guse ◽  
Joel Carton
Keyword(s):  
Adaptive Learning ◽  
Production Level ◽  
Stability Conditions ◽  
Stable States ◽  
Dynamic Learning ◽  
Replicator Dynamic ◽  
Stability Properties ◽  
Price Movements ◽  
The Stability

We investigate the stability properties of Muth's model of price movements when agents choose a production level using replicator dynamic learning. It turns out that when there is a discrete set of possible production levels, possible stable states and stability conditions differ between adaptive learning and replicator dynamic learning.

Stability of radical anions derived from substituted 5-nitrofurans investigated by ESR spectroscopy

1985 ◽  
Vol 50 (7) ◽  
pp. 1594-1601 ◽  
Author(s):  
Jiří Klíma ◽  
Larisa Baumane ◽  
Janis Stradinš ◽  
Jiří Volke ◽  
Romualds Gavars
Keyword(s):  
Radical Anion ◽  
High Stability ◽  
Esr Spectroscopy ◽  
Reaction Path ◽  
Order Reaction ◽  
Second Order ◽  
Radical Anions ◽  
Second Order Reaction ◽  
Unpaired Electron Density ◽  
The Stability

It has been found that the decay in dimethylformamide and dimethylformamide-water mixtures of radical anions in five of the investigated 5-nitrofurans is governed by a second-order reaction. Only the decay of the radical anion generated from 5-nitro-2-furfural III may be described by an equation including parallel first- and second-order reactions; this behaviour is evidently caused by the relatively high stability of the corresponding dianion, this being an intermediate in the reaction path. The presence of a larger conjugated system in the substituent in position 2 results in a decrease of the unpaired electron density in the nitro group and, consequently, an increase in the stability of the corresponding radical anions.

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